38ed7/4

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38ed7/4

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Prime factorization	2 × 19
Step size	25.4954¢
Octave	47\38ed7/4 (1198.28¢)
Twelfth	75\38ed7/4 (1912.16¢)
Consistency limit	3
Distinct consistency limit	3

38 equal divisions of 7/4 (abbreviated 38ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 38 equal parts of about 25.5 ¢ each. Each step represents a frequency ratio of (7/4)^1/38, or the 38th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	25.495
2	50.991
3	76.486	22/21, 23/22, 24/23
4	101.982	17/16
5	127.477	14/13
6	152.973	12/11, 23/21
7	178.468	21/19
8	203.963
9	229.459	8/7
10	254.954	15/13, 22/19
11	280.45	20/17
12	305.945
13	331.44	17/14, 23/19, 29/24
14	356.936	16/13
15	382.431	5/4
16	407.927	19/15, 24/19, 29/23
17	433.422
18	458.918	13/10, 17/13
19	484.413	29/22
20	509.908
21	535.404	15/11, 19/14, 26/19
22	560.899	29/21
23	586.395	7/5
24	611.89	10/7
25	637.385
26	662.881	19/13, 22/15, 25/17
27	688.376
28	713.872
29	739.367	20/13, 23/15, 26/17, 29/19
30	764.863
31	790.358	19/12
32	815.853	8/5
33	841.349	13/8
34	866.844	23/14, 28/17
35	892.34
36	917.835	17/10, 22/13
37	943.33	19/11
38	968.826	7/4

Harmonics

Approximation of harmonics in 38ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.7	+10.2	-3.4	-7.3	+8.5	-3.4	-5.1	-5.1	-9.0	+4.4	+6.8
	Relative (%)	-6.7	+40.0	-13.5	-28.7	+33.3	-13.5	-20.2	-20.0	-35.4	+17.4	+26.6
Steps (reduced)		47 (9)	75 (37)	94 (18)	109 (33)	122 (8)	132 (18)	141 (27)	149 (35)	156 (4)	163 (11)	169 (17)

Approximation of harmonics in 38ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	-5.1	+2.9	-6.9	-9.8	-6.8	+1.6	-10.7	+6.8	+2.7	+2.2
	Relative (%)	-17.0	-20.2	+11.3	-26.9	-38.6	-26.7	+6.2	-42.1	+26.6	+10.7	+8.8
Steps (reduced)		174 (22)	179 (27)	184 (32)	188 (36)	192 (2)	196 (6)	200 (10)	203 (13)	207 (17)	210 (20)	213 (23)